Nonlinear functionals of the Boltzmann equation and uniform stability estimates

We present nonlinear functionals measuring physical space variation and L1-distance between two classical solutions for the Boltzmann equation with a cut-off inverse power potential. In the case that initial datum is a small, smooth perturbation of vacuum and decays fast enough in the phase space, we show that these functionals satisfy stability estimates which lead to BV-type estimates and a uniform L1-stability.